Bowling trio Boyd Rankin, Andre Botha and Dave Langford-Smith are ruled out with injuries.
Batsmen Jeremy Bray and Eoin Morgan have declared themselves unavailable while Peter Gillespie has announced his retirement from international cricket.
Ireland face India on 23 June before playing South Africa the following day.
The squad includes four players who in total have made just five appearances for Ireland - bowlers Roger Whelan and Gary Kidd and all-rounders Alex Cusack and Thinus Fourie.
Langford-Smith has a side injury, Botha misses out because of an elbow problem while Rankin has a stress fracture of the fibula.
Opener Bray asked not to be considered for selection for the two games.
"Eoin Morgan has informed me that he isn't available for the ODI's because of his commitments with Middlesex," said Ireland coach Phil Simmons.
"He wants to qualify and play for England and feels that by obtaining a regular place in the Middlesex team is the best way to achieve that.
"The positive aspect to this is that a number of the younger players in the squad will now get a chance to show me what they are capable of.
"They have the opportunity to firmly establish themselves in the squad.
"I'm already starting to look ahead to the World Cup qualifiers in the UAE in 2009, and the composition of the team."
Squad: Trent Johnston (capt), K Carroll, A Cusack, T Fourie, D Joyce, G Kidd, K McCallan, Kevin O'Brien, Niell O'Brien (wk), W Porterfield, R Whelan, Andrew White and G Wilson.